We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity.We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.

In the past 15 years, the triaxial Schwarzschild orbit-superposition code developed by van den Bosch and van de Ven in Leiden has been widely applied to study the dynamics of galaxies. Recently, a bug was reported in the orbit calculation of this code, specifically in the mirroring procedure that is used to speed up the computation. We have fixed the incorrect mirroring in the DYNAMITE code, which is the publicly-released successor of the Leiden triaxial Schwarzschild code. In this study, we provide a thorough quantification of how this bug has affected the results of dynamical analyses performed with this code. We compare results obtained with the original and corrected versions of DYNAMITE, and discuss the differences in the phase-space distribution of a single orbit and in the global stellar orbit distribution, in the mass estimate of the central black hole in the highly triaxial galaxy PGC 46832, and in the measurement of intrinsic shape and enclosed mass for more than 50 galaxies. Focusing on the typical scientific applications of the Schwarzschild method, in all our tests we find that differences are negligible with respect to the statistical and systematic uncertainties. We conclude that previous results with the Leiden triaxial Schwarzschild code are not significantly affected by the incorrect mirroring.

The observations of external galaxies are projected to the 2D sky plane. Reconstructing the 3D intrinsic density distribution of a galaxy from the 2D image is challenging, especially for barred galaxies, but is a critical step for constructing galactic dynamical models. Here, we present a method for deprojecting barred galaxies and we validate the method by testing against mock images created from an N-body simulation with a peanut-shaped bar. We decompose a galaxy image into a bulge (including a bar) and a disc. By subtracting the disc from the original image a barred bulge remains. We perform multi-Gaussian expansion (MGE) fit to each component, then we deproject them separately by considering the barred bulge is triaxial while the disc is axisymmetric. We restrict the barred bulge to be aligned in the disc plane and has a similar thickness to the disc in the outer regions. The 3D density distribution is thus constructed by combining the barred bulge and the disc. Our model can generally recover the 3D density distribution of disc and inner barred bulge regions, although not a perfect match to the peanut-shaped structure. By using the same initial conditions, we integrate the orbits in our model-inferred potential and the true potential by freezing the N-body simulation. We find that $85{{\ \rm per\ cent}}$ of all these orbits have similar morphologies in these two potentials, and our model supports the orbits that generate a boxy/peanut-shaped structure and an elongated bar similar to these in the true potential.

In the past 15 years, the triaxial Schwarzschild orbit-superposition code by van den Bosch et al. (2008) has been widely applied to study the dynamics of galaxies. Recently, Quenneville et al. (2022) reported a bug in the orbit calculation of this code, specifically in the mirroring procedure that is used to speed up the computation. We have fixed the incorrect mirroring in DYNAMITE, which is the publicly-released successor of the triaxial Schwarzschild code by van den Bosch et al. (2008). In this study, we provide a thorough quantification of how this bug has affected the results of dynamical analyses performed with this code. We compare results obtained with the original and corrected versions of DYNAMITE, and discuss the differences in the phase-space distribution of a single orbit and in the global stellar orbit distribution, in the mass estimate of the central black hole in the highly triaxial galaxy PGC 46832, and in the measurement of intrinsic shape and enclosed mass for more than 50 galaxies. Focusing on the typical scientific applications of a Schwarzschild triaxial code, in all our tests we find that differences are negligible with respect to the statistical and systematic uncertainties. We conclude that previous results with the van den Bosch et al. (2008) triaxial Schwarzschild code are not significantly affected by the incorrect mirroring.

Barred structures are important in understanding galaxy evolution, but they were not included explicitly in most dynamical models for nearby galaxies due to their complicated morphological and kinematic properties. We modify the triaxial orbit-superposition Schwarzschild implementation by van den Bosch et al. to include barred structures explicitly. The gravitational potential is a combination of a spherical dark matter halo and stellar mass; with the 3D stellar density distribution deprojected from the observed 2D image using a two-component deprojection method, including an axisymmetric disk and a triaxial barred bulge. We consider figure rotation of the galaxy with the bar pattern speed as a free parameter. We validate the method by applying it to a mock galaxy with integral field unit (IFU) data created from an N-body simulation with a boxy/peanut or X-shaped bar. Our model fits the observed 2D surface density and all kinematic features well. The bar pattern speed is recovered well with a relative uncertainty smaller than 10%. Based on the internal stellar orbit distribution of the model, we decompose the galaxy into an X-shaped bar, a boxy bulge, a vertically extended structure and a disk, and demonstrate that our model recovers these structures generally well, similar to the true structures in the N-body simulation. Our method provides a realistic way of modeling the bar structure explicitly for nearby barred galaxies with IFU observations.

Within the framework of Brans-Dicke gravity, we investigate inflation with the quartic potential, λϕ 4 /4, in the presence of generalized Brans-Dicke parameter ω GBD (ϕ). We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of general form of the potential U (ϕ) and ω GBD (ϕ). For the quartic potential, our results show that the predictions of the model are in well agreement with the Planck 2015 data for the generalized Brans-Dicke parameters ω GBD (ϕ) = ω 0 ϕ n and ω 0 e bϕ . This is in contrast with both the Einstein and standard Brans-Dicke gravity, in which the result of quartic potential is disfavored by the Planck data.

The halo stars on highly-radial orbits should inevitably pass the center regions of the Milky Way. Under the assumption that the stellar halo is in “dynamical equilibrium” and is axisymmetric, we integrate the orbits of ∼10,000 halo K giants at 5 ≤ r ≤ 50 kpc cross-matched from LAMOST DR5 and Gaia DR3. By carefully considering the selection function, we construct the stellar halo distribution at the entire regions of r ≤ 50 kpc. We find that a double-broken power-law function well describes the stellar halo’s density distribution with shallower slopes in the inner regions and the two breaks at r = 10 kpc and r = 25 kpc, respectively. The stellar halo becomes flatter from outer to inner regions but has q ∼ 0.5 at r ≲ 5 kpc. The stellar halo becomes isotropic with a slight prograde rotation in the inner 5 kpc, and reaches velocity dispersions of ∼250 km s−1. We get a weak negative metallicity gradient of −0.005 dex kpc−1 at 5 ≤ r ≤ 50 kpc, while there is an excess of relative metal-rich stars with [Fe/H] > −1 in the inner 10 kpc. The halo interlopers at r ≤ 5 kpc from integration of our sample has a mass of ∼1.2 × 108 M ⊙ (∼4.7×107 M ⊙ at [Fe/H] < 1.5), which can explain 50–100% of the metal-poor stars with [Fe/H] < −1.5 directly observed in the Galactic central regions.

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